One remarkable feature of wavelet decomposition is that the waveletcoefficients are localized, and any singularity in the input signals can only affect the waveletcoefficients at the point near the singularity. The lo...One remarkable feature of wavelet decomposition is that the waveletcoefficients are localized, and any singularity in the input signals can only affect the waveletcoefficients at the point near the singularity. The localized property of the wavelet coefficientsallows us to identify the singularities in the input signals by studying the wavelet coefficients atdifferent resolution levels. This paper considers wavelet-based approaches for the detection ofoutliers in time series. Outliers are high-frequency phenomena which are associated with the waveletcoefficients with large absolute values at different resolution levels. On the basis of thefirst-level wavelet coefficients, this paper presents a diagnostic to identify outliers in a timeseries. Under the null hypothesis that there is no outlier, the proposed diagnostic is distributedas a χ_1~2. Empirical examples are presented to demonstrate the application of the proposeddiagnostic.展开更多
基金This research is supportea by the National Natural Science Foundation of China (79800012,70171001)
文摘One remarkable feature of wavelet decomposition is that the waveletcoefficients are localized, and any singularity in the input signals can only affect the waveletcoefficients at the point near the singularity. The localized property of the wavelet coefficientsallows us to identify the singularities in the input signals by studying the wavelet coefficients atdifferent resolution levels. This paper considers wavelet-based approaches for the detection ofoutliers in time series. Outliers are high-frequency phenomena which are associated with the waveletcoefficients with large absolute values at different resolution levels. On the basis of thefirst-level wavelet coefficients, this paper presents a diagnostic to identify outliers in a timeseries. Under the null hypothesis that there is no outlier, the proposed diagnostic is distributedas a χ_1~2. Empirical examples are presented to demonstrate the application of the proposeddiagnostic.
